A new implicit solution procedure for multidimensional finite-difference modeling of the Stefan problem

A new procedure is presented for multidimensional modeling of the energy transport by conduction in problems involving solid-liquid phase transition. The method is formulated as an enthalpy model, with a fully simultaneous equation formulation made possible by a novel nonlinear iteration algorithm. This algorithm, based on the problem physics, is easily implemented. The procedure has been tested on a number of two-dimensional test cases, and comparisons of computational cost with the conventional nonsimultaneous procedure have been made for a variety of boundary conditions, Stefan numbers, and time step sizes. The results demonstrate that in practical problems the new procedure is faster by a factor in excess of two orders of magnitude.